Mathematical Sciences: L Functions With Applications to the Oscillator Representation

本文主要研究自同构表示的L函数的构造及其在振子表示问题中的各种应用。将努力将Siegel-Weil公式推广到一般情况。目标是对任何自同构形式的theta对应有一个一般的描述，特别是Eisenstein级数。自同构L函数是各种算术函数的生成函数，并设法在它们的解析性质中编码了大量的信息。获得这些类型的功能如何运行的一般理论是本研究的中心焦点。

This research is concerned with the construction of L- functions of automorphic representations and of various applications to problems involving the oscillator representation. Work will be done to generalize the Siegel-Weil formula to the general case. The goal will be to have a general description of the theta correspondence of any automorphic form, especially Eisenstein series. Automorphic L-functions are generating functions of various arithmetic functions and manage to encode much information in their analytic properties. Obtaining general theories of how these types of functions behave is the central focus of this research.